On the Existence of Periodic Orbits for the Fixed Homogeneous Circle Problem

Details On the Existence of Periodic Orbits for the Fixed Homogeneous Circle Problem On the Existence of Periodic Orbits for the Fixed Homogeneous Circle Problem

2005-02-15

arxiv.org/abs/math/0502305v2

Mathematics

Classical Analysis and ODEs

Scientific paper

We prove the existence of some types of periodic orbits for a particle moving
in Euclidean three-space under the influence of the gravitational force induced
by a fixed homogeneous circle. These types include periodic orbits very far and
very near the homogeneous circle, as well as eight and spiral periodic orbits.

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